Minimum Supports of Eigenfunctions with the Second Largest Eigenvalue of the Star Graph

The Star graph $S_n$, $n\ge 3$, is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(12),(13),\ldots,(1n)\}$. In this work we study eigenfunctions of $S_n$ corresponding to the second largest eigenvalue $n-2$. For $n\ge 8$ and $n=3$, we find the minimum cardi...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2020-05, Vol.27 (2)
Main Authors: Kabanov, Vladislav, Konstantinova, Elena V., Shalaginov, Leonid, Valyuzhenich, Alexandr
Format: Article
Language:English
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Summary:The Star graph $S_n$, $n\ge 3$, is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(12),(13),\ldots,(1n)\}$. In this work we study eigenfunctions of $S_n$ corresponding to the second largest eigenvalue $n-2$. For $n\ge 8$ and $n=3$, we find the minimum cardinality of the support of an eigenfunction of $S_n$ corresponding to the second largest eigenvalue and obtain a characterization of eigenfunctions with the minimum cardinality of the support.
ISSN:1077-8926
1077-8926
DOI:10.37236/9147